Carathéodory Extension Theorem
August 21, 2025
From outer measure to Lebesgue measure: why not every set can be measured, with Cantor and Vitali sets as examples.
Measure TheoryProbability TheoryAdvancedCaratheodoryExtension
Probability Theory (4)
Articles about Probability Theory
4 articles found
Probability Measures and Random Variables
August 21, 2025
An intuitive introduction to probability measures and measurable random variables, starting from lengths and areas.
Probability TheoryMeasure TheoryIntermediate
Borel Sigma-Algebra
August 20, 2025
An intuitive explanation of the Borel sigma-algebra, the key structure for defining probability on continuous sample spaces like the real line.
Probability TheoryBorel SetsContinuous Random Variables
Laplace and Kolmogorov Definitions of Probability
August 19, 2025
From Laplace's classical probability to Kolmogorov's modern axiomatic definition, explained step by step for beginners.
ProbabilityBeginnerProbability Theory